Toward the large-eddy simulation of compressible turbulent flows (original) (raw)
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Subgrid-scale modeling for large-eddy simulations of compressible turbulence
Physics of Fluids, 2002
We present two phenomenological subgrid-scale ͑SGS͒ models for large-eddy simulations ͑LES͒ of compressible turbulent flows. A nonlinear model and a stretched-vortex model are tested in LES of compressible decaying isotropic turbulence. Results of LES at 32 3 , 48 3 , and 64 3 resolution are compared to corresponding 256 3 direct numerical simulations ͑DNS͒ at a turbulent Mach number, M t ϳ0.4. We use numerical schemes based on compact finite differences and study the effects of their order of accuracy on LES results. Both models give satisfactory agreement with DNS for the decay of the total turbulent kinetic energy. The probability densities ͑pdf͒ of energy transfer to subgrid scales obtained from filtered DNS and the SGS models are compared. Both models produce a narrower distribution of energy transfer than corresponding filtered DNS data, with less backscatter. The pdf of the alignment of components of the subgrid stress tensor and the eigenvectors of the rate-of-strain tensor obtained from the models reproduces some features of the DNS results. The pdfs of both energy transfer and relative eigenvector alignment are obtained from DNS and LES after about one large-eddy turnover time from the same initial condition. All tests of the present LES models are therefore a posteriori and none is a priori.
Development of Large Eddy Simulation Turbulence Models
2000
A new approach for a non-viscosity one-equation large eddy simulation (LES) subgrid stress model is presented. The new approach uses a tensor coefficient obtained from the dynamic modeling approach of Germano (1991) and scaling that is provided by the sub-grid kinetic energy. Mathematical and conceptual issues motivating the development of this new model are explored. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES. These conditions are examined for traditional dynamic Smagorinsky modeling (i.e. zeroequation approaches) and the one-equation sub-grid model of Ghosal et al. (1995). It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strainrate to estimate the sub-grid stresses scale poorly with filter level leading to significant errors in the modeling of the sub-grid scale stress. The poor scaling in traditional LES I would like to express my sincere gratitude to my advisor, Professor Christopher Rutland, for his guidance, technical assistance, encouragement and freedom provided to me during the past five years. I also would like to thank Professor Frederick Elder and Professor David Foster for their assistance in the graduate school admission process.
Physics of Fluids
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.
Experimental study of similarity subgrid-scale models of turbulence in the far-field of a jet
Applied Scientific Research, 1995
Several versions of similarity subgrid-scale turbulence models are tested a-priori using high Reynolds number experimental data. Measurements are performed by two-dimensional Particle Image Velocimetry (PIV) in the far field of a turbulent round jet. It is first verified that the usual Smagorinsky model is poorly correlated with the real stress Tij. On the other hand, a similarity subgrid-scate model based on the 'resolved stress' tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale, displays a much higher level of correlation. Several variants of this model are examined: the mixed model, and the global and local dynamic procedure. Model coefficients are measured, based on the condition that the subgrid models dissipate energy at the correct rate. The experimental data are employed to show that the dynamic procedure [4] yields appropriate model coefficients based only on the resolved portion of the velocity field. Some features of the dynamic procedure in its local formulation are also explored.
Physics of Fluids, 1999
The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation ͑LES͒ of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress ͑SGS͒ tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation ͑DNS͒. It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure-strain in the Reynolds-averaged Navier-Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model ͑Smagorinsky plus scale similarity͒ reported in the literature.
A new turbulence model for Large Eddy Simulation
Advanced Studies in Theoretical Physics
The present - day Large Eddy Simulation models based on the Smagorinsky assumption and the drawbacks of the dynamic calcula- tion of the closure coe-cient for the generalised subgrid scale turbulent stress tensor are presented. The relations between numerical scheme conservation property of mass, momentum and kinetic energy and the drawbacks of the dynamic Smagorinsky - type turbulence models are shown. A new turbulence model is proposed. The proposed model: a) is able to take into account the anisotropy of the turbulence; b) remove any balance assumption between the production and dissipation of sub- grid scale turbulent kinetic energy; c) is able to eliminate the numerical efiects produced by the non conservation a priori of the resolved kinetic energy. New closure relations for the unknown terms of the subgrid scale viscous dissipation balance equation are proposed. The flltered momentum equations are solved by using a sixth order flnite difierence scheme. The proposed model is t...
A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation
Physics of Fluids, 2016
Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.
On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet
1994
The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of R, z 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgridscale model. It is based on the 'resolved stress' tensor L,,, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during largeeddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between L,, and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lii and the strain-rate tensor, is introduced. A 'dynamic' version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.